The invention relates to a method for digitally printing a polymer-coated paper or board (1), to a paper or board suitable for the method and to the production of a product package equipped with digital prints. During digital printing, printing ink particles are applied in an electric field to the printing surface formed of a polymer coating at locations corresponding to the print, and the printing ink is adhered to the printing surface by fusion with the aid of infrared radiation. In accordance with the invention, the paper or board (2) to be printed is equipped with an inner coating layer (3) containing electrically chargeable ethene acrylate copolymer, such as ethene methyl acrylate copolymer (EMA), and with a polyolefin-based outer shield layer (4) on top of this, which contains e.g. low-density polyethene (LDPE) and provides mechanical strength, forming the printing surface receiving the printing ink.